A combination of max-type and distance based schemes for simultaneous monitoring of time between events and event magnitudes

Traditionally, two isolated sequential stopping rules are employed for monitoring the time of occurrence of an event (T) and the magnitude of an event (X). Recently, several researchers recommend monitoring T and X together using some unified approach. A unified approach based on combinations of two statistics, one for monitoring T and the other for X, is often more efficient. Likewise, a new approach of simultaneous monitoring of location and scale parameters of a process, combining a max and a distance based statistics, is recently introduced in literature. Motivated by such emerging concepts, we design a new scheme combining a Max-type and a Distance-type schemes, referred to as the MT scheme, to monitor T and X simultaneously and efficiently. It retains the advantages of both the Max-type and the Distance-type schemes for joint inference. The proposed scheme is very competent in detecting a shift in the process distribution of T or X or both. Moreover, it is computationally simpler. It has nice exact expressions for design parameters. Therefore, it is easier to implement. It has a distinct advantage over its traditional counterparts in detecting moderate to large shifts. Finally, we illustrate the implementation of the proposed scheme with a real dataset of damage caused by outbreak of fire disaster.